Abstract
The problem of the avalanche mixing of two fractions of granular material is solved. Mixing of the fractions takes place in a cylinder that rotates slowly about its longitudinal axis, which is positioned horizontally. The cylinder is not filled completely and at all times mixing only occurs in the surface layer of granules. It is shown that, depending on the relation of the volumes of the fractions and the volume of the empty space, mixing can take place slowly, over a large number of rotations, in a diffusive regime with convection or rapidly, by the time the cylinder has turned through a small angle. The mixing process is described analytically in terms of a purely geometrical approach and can, in a number of situations, be reduced to a sequence of discrete mappings. The characteristic mixing times are determined, including the times over which one or the other of the pure fractions no longer exists in the regions adjacent to the surface of the cylinder. Their dependence on the degree of filling of the cylinder and on the ratio of the volumes of the fractions is found.
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